7. \( x^{2}+8 x+16 \)

The expression \( x^{2}+8 x+16 \) is a perfect square trinomial. It factors down to \( (x+4)^{2} \). This means that the expression represents a parabola that opens upwards with its vertex at the point (-4, 0). It's a nice friendly graph, making it easy to identify key features! If you're working with this quadratic, a common mistake is forgetting to check for other factors or solutions if you're setting it equal to zero. Remember, you can use the square root property: \( (x+4)^{2} = 0 \) leads you directly to the solution \( x = -4 \). Keep it straightforward, and don’t overlook those handy shortcuts!